The sides of a rectangle are 7.01 m and `1.2xx10^(1)m`. Taking the significant figures into account, the area of the rectangle is

Options

A. `84.1m^(2)`
B. `84.00m^(2)`
C. `84.12m^(2)`
D. `84m^(2)`

Answer

To find the area of the rectangle given the sides, we will follow these steps:

### Step 1: Identify the dimensions of the rectangle
The dimensions given are:
- Length (L) = 7.01 m
- Breadth (B) = 1.2 x 10^1 m = 12 m

### Step 2: Determine the significant figures
- The length (7.01 m) has **3 significant figures**.
- The breadth (12 m) has **2 significant figures**.

### Step 3: Calculate the area of the rectangle
The area (A) of a rectangle is calculated using the formula:
\[ A = L \times B \]
Substituting the values:
\[ A = 7.01 \, \text{m} \times 12 \, \text{m} \]

### Step 4: Perform the multiplication
Calculating the area:
\[ A = 7.01 \times 12 = 84.12 \, \text{m}^2 \]

### Step 5: Apply the rules of significant figures
Since the breadth (12 m) has the least number of significant figures (2 significant figures), we need to round the area to 2 significant figures.

### Step 6: Round the area
The area calculated is 84.12 m². Rounding this to 2 significant figures:
- The first two significant figures are 84.
- The digit after 84 is 1 (which is less than 5), so we do not round up.

Thus, the final area is:
\[ A = 84 \, \text{m}^2 \]

### Final Answer
The area of the rectangle, taking significant figures into account, is **84 m²**.

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